#include <boost/test/unit_test.hpp>

#include <fc/exception/exception.hpp>
#include <fc/crypto/hex.hpp>
#include <fc/crypto/modular_arithmetic.hpp>
#include <fc/utility.hpp>

#include <chrono>
#include <random>
#include <limits>

using namespace fc;
#include "test_utils.hpp"

namespace std {
std::ostream& operator<<(std::ostream& st, const std::variant<fc::modular_arithmetic_error, bytes>& err)
{
    if(std::holds_alternative<fc::modular_arithmetic_error>(err))
        st << static_cast<int32_t>(std::get<fc::modular_arithmetic_error>(err));
    else
        st << fc::to_hex(std::get<bytes>(err));
    return st;
}
}


BOOST_AUTO_TEST_SUITE(modular_arithmetic)

BOOST_AUTO_TEST_CASE(modexp) try {


    using modexp_test = std::tuple<std::vector<std::string>, std::variant<fc::modular_arithmetic_error, bytes>>;

    const std::vector<modexp_test> tests {
        //test1
        {
            {
                "03",
                "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2e",
                "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f",
            },
            to_bytes("0000000000000000000000000000000000000000000000000000000000000001"),
        },

        //test2
        {
            {
                "",
                "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2e",
                "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f",
            },
            to_bytes("0000000000000000000000000000000000000000000000000000000000000000")
        },

        //test3
        {
            {
                "01",
                "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2e",
                "",
            },
            modular_arithmetic_error::modulus_len_zero
        },

        //test4
        {
            {
                "01",
                "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2e",
                "0000",
            },
            to_bytes("0000")
        },

        //test5
        {
            {
                "00",
                "00",
                "0F",
            },
            to_bytes("01"),
        },

        //test6
        {
            {
                "00",
                "01",
                "0F",
            },
            to_bytes("00"),
        },

        //test7
        {
            {
                "01",
                "00",
                "0F",
            },
            to_bytes("01"),
        },

    };

    for(const auto& test : tests) {
        const auto& parts           = std::get<0>(test);
        const auto& expected_result = std::get<1>(test);

        auto base = to_bytes(parts[0]);
        auto exponent = to_bytes(parts[1]);
        auto modulus = to_bytes(parts[2]);

        auto res = fc::modexp(base, exponent, modulus);
        BOOST_CHECK_EQUAL(res, expected_result);
    }

} FC_LOG_AND_RETHROW();

BOOST_AUTO_TEST_CASE(modexp_boringssl_vectors) try {
   struct modexp_test_params {
      std::string ModExp;
      std::string A;
      std::string E;
      std::string M;
   };

   const std::vector<modexp_test_params> tests = {
      // Regression test for carry propagation bug in sqr8x_reduction.
      {
         .ModExp = "19324b647d967d644b3219",
         .A = "050505050505",
         .E = "02",
         .M = "414141414141414141414127414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001"
      },
      // Cover the E = 0 case for small numbers.
      {
         .ModExp = "01",
         .A = "086b49",
         .E = "00",
         .M = "30d26ecb"
      },
      {
         .ModExp = "00",
         .A = "00",
         .E = "00",
         .M = "01"
      },
      {
         .ModExp = "208f8aa0",
         .A = "086b49",
         .E = "02",
         .M = "30d26ecb"
      },
      {
         .ModExp = "27308229",
         .A = "017591bb",
         .E = "06",
         .M = "30d26ecb"
      },
      {
         .ModExp = "2bdf498f",
         .A = "21292626",
         .E = "0d",
         .M = "30d26ecb"
      },
      {
         .ModExp = "11317167",
         .A = "04a655df24",
         .E = "10",
         .M = "30d26ecb"
      },
      {
         .ModExp = "02e1b88e",
         .A = "da6b761a86",
         .E = "35",
         .M = "30d26ecb"
      },
      {
         .ModExp = "20a12ec3",
         .A = "0ea811",
         .E = "02",
         .M = "23bc042f"
      },
      {
         .ModExp = "c42ced",
         .A = "01011a6a",
         .E = "04",
         .M = "23bc042f"
      },
      {
         .ModExp = "04637d79",
         .A = "28d9a601",
         .E = "08",
         .M = "23bc042f"
      },
      {
         .ModExp = "20e5669b",
         .A = "072fe6bc20",
         .E = "11",
         .M = "23bc042f"
      },
      {
         .ModExp = "142ab9e3",
         .A = "9a07b9363c",
         .E = "29",
         .M = "23bc042f"
      },
      {
         .ModExp = "14c64646",
         .A = "0822df",
         .E = "03",
         .M = "30915765"
      },
      {
         .ModExp = "160e35a2",
         .A = "015ea542",
         .E = "05",
         .M = "30915765"
      },
      {
         .ModExp = "2f23a488",
         .A = "34d2e02e",
         .E = "0e",
         .M = "30915765"
      },
      {
         .ModExp = "28e67f93",
         .A = "0636a32703",
         .E = "14",
         .M = "30915765"
      },
      {
         .ModExp = "29bfeaa5",
         .A = "c8646998e6",
         .E = "2c",
         .M = "30915765"
      },
      {
         .ModExp = "30959e22",
         .A = "081dad",
         .E = "03",
         .M = "326dd68d"
      },
      {
         .ModExp = "1a1da4fa",
         .A = "0116adb9",
         .E = "05",
         .M = "326dd68d"
      },
      {
         .ModExp = "272bf0d8",
         .A = "2d21ef08",
         .E = "08",
         .M = "326dd68d"
      },
      {
         .ModExp = "29f5054b",
         .A = "076989850a",
         .E = "16",
         .M = "326dd68d"
      },
      {
         .ModExp = "0e6c7b77",
         .A = "b88ee70d2a",
         .E = "3e",
         .M = "326dd68d"
      },
      {
         .ModExp = "369605e1",
         .A = "0cf26f",
         .E = "02",
         .M = "3ce082eb"
      },
      {
         .ModExp = "168a3c5d",
         .A = "01f82caf",
         .E = "05",
         .M = "3ce082eb"
      },
      {
         .ModExp = "125c4bb8",
         .A = "2e9c4c07",
         .E = "09",
         .M = "3ce082eb"
      },
      {
         .ModExp = "1c5fe761",
         .A = "0523ab37f1",
         .E = "14",
         .M = "3ce082eb"
      },
      {
         .ModExp = "21703009",
         .A = "dc832165e8",
         .E = "20",
         .M = "3ce082eb"
      },
      {
         .ModExp = "01228d1e",
         .A = "0a5555",
         .E = "03",
         .M = "24665b27"
      },
      {
         .ModExp = "05226af4",
         .A = "01077bd6",
         .E = "04",
         .M = "24665b27"
      },
      {
         .ModExp = "1b14eac1",
         .A = "2db3a834",
         .E = "0f",
         .M = "24665b27"
      },
      {
         .ModExp = "161727bc",
         .A = "06bd962cb6",
         .E = "19",
         .M = "24665b27"
      },
      {
         .ModExp = "10d61d0d",
         .A = "c10caed407",
         .E = "28",
         .M = "24665b27"
      },
      {
         .ModExp = "233da406",
         .A = "0b125f",
         .E = "03",
         .M = "33509981"
      },
      {
         .ModExp = "24032799",
         .A = "01656b7c",
         .E = "06",
         .M = "33509981"
      },
      {
         .ModExp = "129ecebe",
         .A = "2e671504",
         .E = "0a",
         .M = "33509981"
      },
      {
         .ModExp = "20c20bac",
         .A = "04d7a2de44",
         .E = "1f",
         .M = "33509981"
      },
      {
         .ModExp = "2e3ce9d3",
         .A = "c53b3def4d",
         .E = "31",
         .M = "33509981"
      },
      {
         .ModExp = "12fadfd6",
         .A = "0b4cf8",
         .E = "02",
         .M = "36e9d4ae"
      },
      {
         .ModExp = "0457ac85",
         .A = "01b1c7e9",
         .E = "07",
         .M = "36e9d4ae"
      },
      {
         .ModExp = "31debef4",
         .A = "3a973028",
         .E = "0d",
         .M = "36e9d4ae"
      },
      {
         .ModExp = "2333ad93",
         .A = "0552b97c45",
         .E = "11",
         .M = "36e9d4ae"
      },
      {
         .ModExp = "099ba1fb",
         .A = "8bfb949cbb",
         .E = "28",
         .M = "36e9d4ae"
      },
      {
         .ModExp = "27b691de",
         .A = "093492",
         .E = "03",
         .M = "298fdb16"
      },
      {
         .ModExp = "03c2b70f",
         .A = "014e7b0d",
         .E = "04",
         .M = "298fdb16"
      },
      {
         .ModExp = "1486cda7",
         .A = "29acff81",
         .E = "0c",
         .M = "298fdb16"
      },
      {
         .ModExp = "11725275",
         .A = "0507489205",
         .E = "13",
         .M = "298fdb16"
      },
      {
         .ModExp = "24d14627",
         .A = "e71c55606d",
         .E = "35",
         .M = "298fdb16"
      },
      {
         .ModExp = "222b8d14",
         .A = "09b1a0",
         .E = "03",
         .M = "3db59d12"
      },
      {
         .ModExp = "3b8bd47d",
         .A = "013f4e8d",
         .E = "07",
         .M = "3db59d12"
      },
      {
         .ModExp = "17e72356",
         .A = "334774ce",
         .E = "0a",
         .M = "3db59d12"
      },
      {
         .ModExp = "306447ca",
         .A = "047079ddd2",
         .E = "12",
         .M = "3db59d12"
      },
      {
         .ModExp = "090bef3b",
         .A = "a75d62616d",
         .E = "37",
         .M = "3db59d12"
      },
      {
         .ModExp = "01",
         .A = "cddd44f47e84b3276cc36a5c0d742cc703e61c4756168601fbb1b6eb598c161019562344dd56ab6f603d920a12c360b285e6496a3605a2f8d691c3598233ee9366b5f2692554893bdeb67b7bdaf35ab7273ac593145e26bed82c70ba5793bf4bc5cac4c80b01785d1496beede493806e4f4aa89fd8d41de80dd6d0a3e2742678",
         .E = "00",
         .M = "c95943186c7567fe8cd1bb4f07e7c659475fd9f38217571af20dfe7e4666d86286bc5b2bb013197f9b1c452c69a95bb7e450cf6e45d46e452282d5d2826978e06c52c7ca204869e8d1b1fac4911e3aef92c7b2d7551ebd8c6fe0365fad49e275cc2949a124385cadc4ace24671c4fe86a849de07c6fafacb312f55e9f3c79dcb"
      },
      {
         .ModExp = "00",
         .A = "00",
         .E = "8de689aef79eba6b20d7debb8d146541348df2f259dff6c3bfabf5517c8caf0473866a03ddbd03fc354bb00beda35e67f342d684896bf8dbb79238a6929692b1a87f58a2dcba596fe1a0514e3019baffe1b580fc810bd9774c00ab0f37af78619b30f273e3bfb95daac34e74566f84bb8809be7650dec75a20be61b4f904ed4e",
         .M = "c95943186c7567fe8cd1bb4f07e7c659475fd9f38217571af20dfe7e4666d86286bc5b2bb013197f9b1c452c69a95bb7e450cf6e45d46e452282d5d2826978e06c52c7ca204869e8d1b1fac4911e3aef92c7b2d7551ebd8c6fe0365fad49e275cc2949a124385cadc4ace24671c4fe86a849de07c6fafacb312f55e9f3c79dcb"
      },
      {
         .ModExp = "5150fb769d5c5d341aaf56639a7bcc77c415fe46439938a2190283409692f29cd080bfe3433005d98d24718a03a3553c8560c5e9c8ed0f53b8945eb18290e1c1a83d919302510f66dd89b58acc2de79ad54b8a30d3e1019d4d222556beefca0821b094ecf104b5e4cfce69d2d520d2abf54f3e393d25ed3d27e8c2e3ca2e5ff9",
         .A = "ead8c5a451541c50cab74de530c89376d9a55c723e0cac3c84b25f0093c08a2961e49ab48966361c42c9f99111587252d98395b76788400d75c66ef208ea2767a28d6f8dc3a859f39c95765d57f139e7fc14f47c908c62df051e7216d379f52028843b4d82ef49133cce8fe671ae179423ac8da5be43b01caaf425cd969300cd",
         .E = "8de689aef79eba6b20d7debb8d146541348df2f259dff6c3bfabf5517c8caf0473866a03ddbd03fc354bb00beda35e67f342d684896bf8dbb79238a6929692b1a87f58a2dcba596fe1a0514e3019baffe1b580fc810bd9774c00ab0f37af78619b30f273e3bfb95daac34e74566f84bb8809be7650dec75a20be61b4f904ed4e",
         .M = "c95943186c7567fe8cd1bb4f07e7c659475fd9f38217571af20dfe7e4666d86286bc5b2bb013197f9b1c452c69a95bb7e450cf6e45d46e452282d5d2826978e06c52c7ca204869e8d1b1fac4911e3aef92c7b2d7551ebd8c6fe0365fad49e275cc2949a124385cadc4ace24671c4fe86a849de07c6fafacb312f55e9f3c79dcb"
      },
      {
         .ModExp = "01",
         .A = "935561297d1d90255aef891e2e30aa09935409de3d4a5abc340ac9a9b7dce33e9f5ce407f3a67ec30e0dc30481070823f8542463e46828d9cafb672a506d6753688cbad3d2761079f770c726c0b957071a30876c4d448e884b647833befbcd6b582787bf769d63cf55e68c7b869a0b86374f8920516cf5d528f348b6057450a1",
         .E = "00",
         .M = "dcc24236a1bb94c71d9ec162a6aa4697b932717e82b667cad08b6bd1bbcbddf7cd167b7458de2b0b780486b39574e749d6405f9ede774a021d6b547271523e9e84a6fdd3a98315607ccf93356f54daa9c75e1e311e1672d0dc163be13f9ed6762f7dd301f5b0a1bb2398b608f40ac357ae34fc8a87d4fef3b961cbdb806d9061"
      },
      {
         .ModExp = "00",
         .A = "00",
         .E = "bb552be12c02ae8b9e90c8beb5689ffefe3378d2c30f12a6d14496250ecce30317c642857535a741642c3df689a8d71a276d247ed482b07b50135357da6143ac2f5c74f6c739c5ff6ada21e1ab35439f6445a1019d6b607950bffb0357c6009a2bfc88cd7f4f883dc591d4eb45b1d787e85aba5c10ee4fe05ea47bf556aec94d",
         .M = "dcc24236a1bb94c71d9ec162a6aa4697b932717e82b667cad08b6bd1bbcbddf7cd167b7458de2b0b780486b39574e749d6405f9ede774a021d6b547271523e9e84a6fdd3a98315607ccf93356f54daa9c75e1e311e1672d0dc163be13f9ed6762f7dd301f5b0a1bb2398b608f40ac357ae34fc8a87d4fef3b961cbdb806d9061"
      },
      {
         .ModExp = "bbad67352704a6321809f742826bf3d1c31c0ad057bf81432abeb30dc9913c896c03e69eb1cde6b78ffcb320c4625bd38ef23a08d6c64dc86aec951b72d74b097e209ce63092959894614e3865a6153ec0ff6fda639e44071a33763f6b18edc1c22094c3f844f04a86d414c4cb618e9812991c61289360c7ba60f190f75038d0",
         .A = "855144760f2be2f2038d8ff628f03a902ae2e07736f2695ec980f84a1781665ab65e2b4e53d31856f431a32fd58d8a7727acee54cc54a62161b035c0293714ca294e2161ea4a48660bf084b885f504ad23ea338030460310bd19186be9030ab5136f09fe6a9223962bce385aaaf9c39fe6ed6d005fa96163fe15cdfa08fc914d",
         .E = "bb552be12c02ae8b9e90c8beb5689ffefe3378d2c30f12a6d14496250ecce30317c642857535a741642c3df689a8d71a276d247ed482b07b50135357da6143ac2f5c74f6c739c5ff6ada21e1ab35439f6445a1019d6b607950bffb0357c6009a2bfc88cd7f4f883dc591d4eb45b1d787e85aba5c10ee4fe05ea47bf556aec94d",
         .M = "dcc24236a1bb94c71d9ec162a6aa4697b932717e82b667cad08b6bd1bbcbddf7cd167b7458de2b0b780486b39574e749d6405f9ede774a021d6b547271523e9e84a6fdd3a98315607ccf93356f54daa9c75e1e311e1672d0dc163be13f9ed6762f7dd301f5b0a1bb2398b608f40ac357ae34fc8a87d4fef3b961cbdb806d9061"
      },
      {
         .ModExp = "01",
         .A = "9d92629c1ab181c50c31619e8acd0d235a1f5fc7a0bef4d4fd54b4f1968d45921f8522efe88e69c6c14c576c564592b9feb00d1554b88b038934eaf4a8ce81a2582732387490181ef158360c8b2d9ccb326ffe043f776a50cb8202837f08ca743b562eefa007150ab7012c341b16248478d4775c02ad71ea13d5e82b71e2d600",
         .E = "00",
         .M = "cd607549668469b792f495c141e500871880b0611c8004293a561ec7f9ab6561f8a9b90872742386adafb5cd1890e8204ae12aec529cca0a9e382c96439137f09de9973b12c8492c62847e107deabb7dd946ffbb9d0ac73b462c481092bd65326a17f21d8d6527c47a5dba50aaa20c7048b8788a49eb3ea5f29bd5cfce24eb3b"
      },
      {
         .ModExp = "00",
         .A = "00",
         .E = "9f43dcb641f3ecf4dbc97450f2bdf3b7ec6a2f3e8e96bb1df2bf34b8d2d78e1a9018d04d960ffd0e932cfc60d3b9b923e3f9f29b3f3d61cae3a9f7245078143475c7fcb896ff200f7d94c4f2708bb42750e37c185a31c876814e4f06a00771707654e1da2fb69c16b6500b16385e3b933e2276ad3569977473f699b1c7926c3b",
         .M = "cd607549668469b792f495c141e500871880b0611c8004293a561ec7f9ab6561f8a9b90872742386adafb5cd1890e8204ae12aec529cca0a9e382c96439137f09de9973b12c8492c62847e107deabb7dd946ffbb9d0ac73b462c481092bd65326a17f21d8d6527c47a5dba50aaa20c7048b8788a49eb3ea5f29bd5cfce24eb3b"
      },
      {
         .ModExp = "24eaead5b57883c2f454928f8edd470a344bfe07a953194f7d635d705ef13ddfc64140c8ad6f363d4c828e7c7891a6b6d4df37335de4552c319dafd1c06d1f743240082a3535df4da1475d3eea3fead20e40815fd5a0876c881c162ab65a1eda494280c258901ca953d1d039a998bf0e9aa09273bbef4865f3054663b72d75ff",
         .A = "a31618b4532f53729ba22efb2221432fab1dbb70853d6a1159b42fd19fc949965c709b209de106a652aa422d88922ce51dae47f7f6deaf0055202e13db79ee84fc3d3c6f4c003ef96597c49d6895fa53c22ac9e4819f7048146b5272f6279424fdb389819a0b251c823c76f4bebf4f1246de455aafe82a0d34454f5039e90839",
         .E = "9f43dcb641f3ecf4dbc97450f2bdf3b7ec6a2f3e8e96bb1df2bf34b8d2d78e1a9018d04d960ffd0e932cfc60d3b9b923e3f9f29b3f3d61cae3a9f7245078143475c7fcb896ff200f7d94c4f2708bb42750e37c185a31c876814e4f06a00771707654e1da2fb69c16b6500b16385e3b933e2276ad3569977473f699b1c7926c3b",
         .M = "cd607549668469b792f495c141e500871880b0611c8004293a561ec7f9ab6561f8a9b90872742386adafb5cd1890e8204ae12aec529cca0a9e382c96439137f09de9973b12c8492c62847e107deabb7dd946ffbb9d0ac73b462c481092bd65326a17f21d8d6527c47a5dba50aaa20c7048b8788a49eb3ea5f29bd5cfce24eb3b"
      },
      {
         .ModExp = "01",
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      {
         .ModExp = "01",
         .A = "fe9f77f7d0475e00ec964c0effb9b8e079c32e376ce77a9c40ce4018c3df44a77b4f294d9565502b2b79accb30cb58dda6d15e1543b6d4a53296543ed11c7f51baab60283ef03fae37dfeacb431392487ec2839551a933895c4dbf18844f7b375d3e6f558d3c39993cea1bbf7fb743a6a07bd3753c03eb7298811476d7f3ff1d",
         .E = "00",
         .M = "e7a96cf6fa930f73c8bdc2726bbba246001a9d27f39cc2b978c99dc6f15af0e8aaf26b565302f1112e607e2df4066948baba931b89cd9bbdea2072e05b9a4968fdf282c43d997987c3a3a0434e925a679ac81f316b7a7b724b79be3d6888b66f4512759bf66cfaaa88b9513dd27a44aaea75437268a014c4eb50ba2e50093511"
      },
      {
         .ModExp = "00",
         .A = "00",
         .E = "a0bc148ed50a9b54036bb8fa1f214979052ebd47db8b347af3bb03b806bb457b468ba34781f8a25f289a7a90af4903dc14809a166df2f4c3527de2ea6911cb1afb9071a4afbb522a7d50634d66fd584c73f32d05217dc9f7f16394c68a692a953492ca85f89cc11da95fd8cac6231647923ced48a1b3b0ee68c010286d452836",
         .M = "e7a96cf6fa930f73c8bdc2726bbba246001a9d27f39cc2b978c99dc6f15af0e8aaf26b565302f1112e607e2df4066948baba931b89cd9bbdea2072e05b9a4968fdf282c43d997987c3a3a0434e925a679ac81f316b7a7b724b79be3d6888b66f4512759bf66cfaaa88b9513dd27a44aaea75437268a014c4eb50ba2e50093511"
      },
      {
         .ModExp = "91fd879d02f95a9f40fcd1037726f73892caf84e9b43b4aa4126d9062a0d22c464e7af2fbd91aa849612d99d9519b724a7fb1cb018fffdcff321d883ab2519953c9f174f09dd8f13ac87339887385966eb4a94842276637b2c36c0a5036b1d3bbea438bc6efd4b4851c7ec06879d60694df894717569bcd31c4b13d80df6cbca",
         .A = "cdec5edc1cb3ea974342b85aabc0f9385cf877ca328747d40dd4d297623ad69ab6582653faeed5aef225208305135cfbee32e066cb43e18afacea3a32acc8aabbc49617ac33e741651924ae56dd6aa044a12a1ea50fef573b5befb2f4b21b9cf83ab2aaa6fd153580a0761666ade8fb94f202a3c3dc4f33297eabb4564374168",
         .E = "a0bc148ed50a9b54036bb8fa1f214979052ebd47db8b347af3bb03b806bb457b468ba34781f8a25f289a7a90af4903dc14809a166df2f4c3527de2ea6911cb1afb9071a4afbb522a7d50634d66fd584c73f32d05217dc9f7f16394c68a692a953492ca85f89cc11da95fd8cac6231647923ced48a1b3b0ee68c010286d452836",
         .M = "e7a96cf6fa930f73c8bdc2726bbba246001a9d27f39cc2b978c99dc6f15af0e8aaf26b565302f1112e607e2df4066948baba931b89cd9bbdea2072e05b9a4968fdf282c43d997987c3a3a0434e925a679ac81f316b7a7b724b79be3d6888b66f4512759bf66cfaaa88b9513dd27a44aaea75437268a014c4eb50ba2e50093511"
      },
      // Craft inputs whose Montgomery representation is 1, i.e., shorter than M, in order to test the const time precomputation scattering/gathering.
      {
         .ModExp = "9442d2eca2905ad796383947b14ddfcc341f5be8fec079135c36f6f0d9b8b2212f43e08bf29c46167ff0fe16b247cd365df4417d96cc31c94db1cf44b73b0ee3ebcc4920d9b0d003b68e49c1df91e61bc7758a8a1d2d6192ff4e1590b1a792f8be3a1b83db3ad9667d14398d873faf5d885ec3a2bef955026fae6dbf64daea2b",
         .A = "3a4b4c57e62c5e9d1a9065191f8268fed9d5f6f424d071acef66f0662b8210f4c029ed991512e40c9c912043c816d2c4c5b53fa0e5c253e16808aad4225130dafbbb89fd4f30cdfc1c2f2179b636a7ddc4be579795820b4b9377637bd8a21a0ef5a90d0e0f865321eee23d9be2a3b7320b4012d02941b892df2c40bdc85c1898",
         .E = "a2c56ea1362511cac0301918e15a9afe7d37edd438a5c3538d258ea01f0a6df758de07111e868b3ad8fc89b629b4955d78a1b3af902be1806410ddde25ccc6a196ba5949395c1ad5d8725b18815dc1cd5ac1c7dd17773f571e3f2e628255af14476e0494be23a4a4dfd18e23142f33d7a59c236fec61660e360d9676a747c69f",
         .M = "ede35a3a7afac817d413373a2032abbc067b1493f709ae6e1282ee5469743391d891b904938857168802b7872d3cd7ac18ab249a9e540a86f970b1d0f310a4cc29df1cc9d4063d98c554f1a32f4ca5eba3523cdfb142e0fc609907c7a92bb0187009d97ec471db3545f42dd5fd29c07b7816085d09477ba31fcf90084660116d"
      },
      {
         .ModExp = "a7f5844fa9e7202d4b70ee252c9846e63d3d091b0387768ded872cec53458e19df0d9b4960226e269b8ca5dd4c4eda423a67b6dbb48235c08c12c6c7c78db47287756d3ed9cecb9232f7d18d5d80b9676cb68ba4a290c97e220beb1a069976b5e6022a4c1e5ddbeec86b62dda24ffea1deda37695c9f61a8817218e6370c0679",
         .A = "7d6d0cc947ceb949cdc4e9e1044f5deca5bb05a491041e0d85bc4b92a0944a57c72845fad91e59010c61ad1712bd2f612d53a846a044632262a9f2e3373b062fde2484e0c165ff947f2469f743ab6e2e5e13c640fc4029b1c9213eb8473c674e7f9e95a4a5c5636d4656c1e696962340d77b322daba47d6fc894f2a2cd9e0afc",
         .E = "b78012afe806e2344d004c739c97324256850980ac97d88c4ed9a838517639ca112e235978d21a176c33f5a68703aba0f2a05501bbe3fc8d49a000fbf530cdb431581dfaf8683cb15a2aee5e239cbc542827100da3b47babf4a16ca7c588aff9912e674abb449e0b767a15e415f4e7f2bbd6380d7131da3df8d49b13bfd35ce3",
         .M = "b72d5c55bd2998472f1965e75a51be6155c1ba04656da8f66bcb34db36a7b1db66a89d1d05b1bde10206acf85be7b474ab689220faf1bb52ab39d8dc00512dd4e26df1179c11b973e1274db85a88c7cc2a17113abdffe58cb930ddc5f3ccc4d68b4e65c913730509f7ce5656e8bbaba9b1be177ab9f766678f018fea05da9cdf"
      },
      {
         .ModExp = "465ff295786a88496828fdc763e9292d557957544e9322b7996807b87fdbfa7a11614bffeec557ca831c4824c8e4ca3b1a1c7f3f4f95ec3fd6a86b73bb13d78b73af2b3c7e76954d0cc03bcb0cd606867ebb3765a8b3d0108cbe4f343a14016be9c33f6d200f0dc547e7d6b02bfab1e79dcdf9c9835a814cc6c855a12ebeb66d",
         .A = "89ad02bea3e9ab839a6e23f20122409daba52c68e1e893034b30d321c0305434a6af940015e3fa5ca9c35230da34beeb1ed4fbce6c1da3a8bfe3f3ae172276c1d1723b47ee61e6f8fcfdafad102d6f7ee2a79f510c7edb93096205a40a6c9e665b88b18f39a979e2e61286d939952a6f02fe8148b7515bb25f4252337cb6e60d",
         .E = "cbd6ac628cc7afa3c61bee9c22a06a395087ec1811fe9681b55216700c435996c815e7cec8aaa90016dd2382d0306a5414630124e14f3d396a4ba02ee17851bf720f1607ff813e4bbddf01338983db12f59bd6371a738eee3eeb716f21051d6174d2d6c77602942b9edaac18d4b3a723096c0d00dd23a8a605c585022f311560",
         .M = "fa7a3e40364c8a8d0f14f0213a3f3e035222ca0ea19d46d10ba41580e5dd2805c8a133f3856d7d5d97f922ea540e5eb0d10ad04dfdbb74f518f58da0099a6fc2b3f3def92985176e07fc78aff2faebccca10a429794e5f15ff92f75fe90f527c60ddea8093a9078c703c372ca09f7aeb27ade02f3595308c61dd9c44e62fd101"
      },
      {
         .ModExp = "cf08bf00261402102e9fe03f3074471dcf0e9b3c96d4d1503f099f24ec85e1901b023e9e048c1ad042244f5f70b38b25a99f4c0a7b57d5844bb0d0137367f45f4ce2cc7746105b77414768cb97648dc5721149aed2d4c682408cc0d50d26dd0bd77e848911f8625c727cac5f32e63bcb548f41a57d718d772f23983a42f603bd",
         .A = "a419646a6631c2c69b18f7aa65011825eb31692eecaee9d74f92d92203811b68e9764bda31a1585bdf69b6273fc6f9f508c395ac081336506525dad88473512f08a205621ac8b16e9864c7a7c5a4f17435de00d0b32badec6ce4897e3e1076c562b6d9523f63d0b2079eaa416cb090471657763f24931d955d1fa2720c80a9c9",
         .E = "d5a6f4a1842aaee39805356dc8d0d678ee03b2c81277345beccb2742f899132feb43271f95968a01ae68aa8277201851992dc0aa7a71c90aae71b124d873ee264ea400fb131be0fc6c4ce8c04c45f6bdaca89ac743635caf6158983d257e21cef6800d7f990e912ba21bbfb8fb779afa4abd19e07e7e07eee9908493d1ca502c",
         .M = "e739689b6cc6def1d45fb1a2ab551643beeb303f4aaa4da47ee5e4948510f8445b4c40e99ae8354dede60b2ba6694e93bc4d573b7e8adf871b7a9a9636eb7d70f2e49328e2d7978143b177cee8374ef01bd1ee2d95862765883f5e7971668b53ef0ff41b6539faf63c397522b0bdce916388e72e26c8d3d2e58dadeb9eb5d479"
      },
      {
         .ModExp = "827e6312ec3b14600203bb83f5b277ded197b2967363630ef673240df05edd3ba8ab2b11c86251a612206569c6c33952b31e264f129909bfe723bd0ee1624b36cfcfaa893a6ec8b5a1f7de79f83e79b459a3350f89f412ad1cfd6bc4c2a7a29272c783d6ecceeb1398fa17041835643f4debef9b5e87b098d104bb8912dddf7c",
         .A = "b8e49c637829021d32db3a39a0c1e58cdd4c6e4eda7e8e9293be379e9c2e2d184f929d278598a81ae231cfedcf69cce4a6e31cda3c8ac14d753a7311f2436e29795f0dfb60259a0f61a997918ff984aa2284b43a9d64c974059e9682adfffd018305835f74eda8c75fe4877d811c1620f654ec9f7f32d1af5ce59115e2f41785",
         .E = "80e0febf369d234bf1aaad4f82df2e2ff02882c3184781f6ccdf4f7cd93b6887af86830077c84dfb02109ada05b40970b1c65228b0c19030bd6361c3537fee22a8155c03b4e7007ca006c6daa3659518d05bb81ea0079456d0ef6116df248dffdb0c935f321f5a1034deefd5a9414a0652aa6548de33325b474b9e5a8507a082",
         .M = "d5eb1d14af842a9973274f7463d90cf0ccff19c47d710edbae184478d4f29b02693ed7958bd487054327b9e6d8879e24c9af7730b92f323eeac05558da6c1b952e5dbf13de236050a77628bb5325fe0d14cc5773bf73338759d5ab43c212b414581280f1cee250007e53791b800b61c90de0328acd7bc43fbdda48158939392d"
      },
      {
         .ModExp = "4a1efd29c7e78549f5cd4deed1454b37462c7810ee6a8a2493b764dfa479be13b314cf9ff98259517d61865567ef499a511630c0038c97914625df181c6fe07892f329f98b344a78d751e9471483eebaa7977371bf97bb25187ae7e93a9227d6c124ccb4644423c961a11ae59c4354f89d5a95164c23d9aa256e289e9cc0858e",
         .A = "bd86c9211fa6a47a06e5016c46cb8a99e34a043a29e22f8c3196fa7197c26b38927b8d9bc0ddc11a5fa4bcc44deb69dbf37cbe7ebc9a2fad6c74e09ab5a9dd929fa04ab4319b6caad1035739be78ba631fb0748d9e53944836d37ccda6e6a62823c696d8f31139ccd7f2f86b22fa026ecf433cfb1271a3539ac4f1c83aaac059",
         .E = "c40b9972006d28a84c2769a86e526a2b274f73afc7c5c6a2742166757f61b5f5fdbb228afa157af62af989ffe966f232bba9e6beef5403d1690ade31a6410f7f349a35bc4267a129afd647993df7d45cc0e1a1ba4678d7f1b6e8a344d8ff7037679e1f4db25a454e4246f6b55c416567fcfa188e8a3865115851d9edf0aa8902",
         .M = "cf424d7af75ce7eef90cad75ae55ca8810cc7b4703fdb5bce701e7bac07e0c371cae06df2aa8facb55a0faa6793e4d2bd9d7969703743b9be170be82792aeea55e2bc0f7ab7617b276486bf474dee2f4556aab595ff3ef115139cfe5e21ccd4ee05c0e1cf901bd85df86cc17195a783b0be836d00bee82ce064077f9191188f9"
      },
      {
         .ModExp = "3137a3049fd4ad2e26d870f5c998cf11bfe82101884a82e85e43facd0928cd7434a2e346ca124619769fa141bbe92ad6f36b99231032ddaec3b349a410f82b5ca36f45e56e5fb85dc63d32053dc90805d3f1854ab385281a71a57726bf97158494e7476057214ca7379ab8b70f5bdc15f70bdad3adf33c3a1f9cd1b6bbbad556",
         .A = "039a1dc6a4c3f14d9c350ee968d5ce139ef725952c967a2d1bedf48ace22091283525be03807e2e263d2640be77f0525247bcd07149bba50568cec5a082c87d72962cf9e43bcb5cdb1e7e9a650fb53e0ec2fad37f09a9f036c0d7dfa528fef846769f80a9a60854910ca1b4ee05dba82ed2ee018348d6b3e52a764b8ffae61e0",
         .E = "deaee3a3f80c9f684ed7110c0653847ccc7be5ff6d982fd4b49f59b5dd35f7210b1077babbcedbc127df35cd469dc6e569a0f84e58149b5605c94b09fd7f0b098d02b4a04631328b3fae39e6c2fce25334225cab71829abdb9507cb903701559660f2c08c3b743336119d1260a0db27054cad3f28bc1b04b2289baa58fb33965",
         .M = "938388927d06ed3bb1286c0f06d3054cb0ee16dc7a0bbbf13a45293c09a5f40f1d611b2e1a1b0ec2ef109b508e27af4274954905cae52034f8740a744153b4d22059f0dd262ea51785522098ecacced6da07709ee6b5acc8c4e99331379a7c3de7f4e2d1431e43b19570140955b7bcba118dfbaa552cbfa2be531e8f781166ed"
      },
      {
         .ModExp = "c15ae334455d9f4d1030cd33e734726a27c63624c2afc576238cce5e0498298a4a0c93090a0d19568b41290303c4b558f3d9dd74f9cde8798710f68569ea0d6fd971ce67ec5b54495031de3d8842b8b49288725bee5c9f72b99054d64986ccd4e18d70d5f33943f08cd694eff538f84438ea993ebaba0910c95b3a694f213510",
         .A = "def633b955a917569df3ba8517455eef0655e7a35985edda27097a063e0d82c7c3a76dc36c5d8a71ba9d540790ddd0ea514aaed98925f9a1808eb288d387aaf9605a9ef8a333ebee7ad7057bca012efd619d5867f02266f65976ef4b16da17468426ac4f99b3e8921707e01b4de20f6f9a068e6a19d872079a27f3a44449db83",
         .E = "a465c47b0d15d48e01bb8b1d8e3b3253e11515f6874dbed6c25818adf1a8fd927124d5593beb367f685c11e46f18415be73ccdf16fa2e93a600b728163d21d232849e5278c3749d903edad3f1c4535a2f55a2ab65e7ebc64888bd2a0527e876ecf38cec3ab1980d08138709fad8eb88ae65d960adc3f0f8e92f784fe96fcb693",
         .M = "e43cb9ac1446154356cdc31ec771c79b0e461e22d95185bbe1a279c0945e3af07903a0cb54d553380716fcdcafb4b7cf5dc6da481dc74a8c583d75ff6c1f8e429182d200246ebc473bb56e173787987c1b7fb2dd23f5b2e438a97bc4a1df628bc044fdd1e80c0cf37030adb7b04784dab827d0dcd64f0dbf37c980612570ce11"
      },
      {
         .ModExp = "75c3f79ab7c991b98e65505342a8a563cfb08b5d3ccf8664c7db1de50256b1d17ebf7096dc98c7bb5d7f027a894ae5cbb14dee04d5d445e775ad7e239acc82673b0ac2d819a69c83864f34e73d9a636f05de8279619a067b4c90ad038db5910447e03841d2034635018f08cbcd21efa00994247763a249082594128112f95232",
         .A = "34def7d76f6f158a359fd12759fb889cdf6af0a24830dc3e84283a1ab4e9b2647a6a36b86482f829b2cdf3e3d6028f9a884b1f64f7262315446bea8b0231828e2f3d990fb103c17f820b39e4b8427c85643ceeca8f5dc8f191d1255768300e859bd7d88c770319ef38269660d221cb3bc061389b6fc0783485ef042b1c7d6fef",
         .E = "c6c46453dd5aac6b37277a446b1d0c69cbe476eeff55b3ac35edb89ba97116b0e7783660f2c7b31b2a2d6c4709d0ab45d01a838100694b0777c9c9c14c959b07c437c73a5eabb7402f1001e802d797a2e7707285834fb6440a1c2f727f7bb84ddb2a49312d32fa0ce620c43872655cb5c394749c9e75d7fa25be00efe50d47d6",
         .M = "fbbab6698a9142095c46b38a732592e4366c1838b84bf40f8c8fc7b630f73380a0d09765562365798f8c8030ed1b6728329d8bb06e882c35a1d59bfe84146a9db2afe42a414014e247390281c782fce806d62adb54778d2bcb49555459429d6ed446af5359657667f6aa19e8e3e0e24ab2bc312b2d90b5cb1ce6f2f15af15d9d"
      },
      {
         .ModExp = "ba16d7f3f6e162ce248490d164a13c00e7720d8a667e2d3ebeb13f1663e15ef5408d5b56cbc7bc793a8ca787cc50f8e15e0e9d4ee764531d04a9114eea556bb3e206ed7d85267151a056b6e68fbf35e03f2cf829708ffe1de13e95ecfe365aff1eea36340ffcd3892dee659fb1ecbe50f5080e54737c10f9c1ba638b14ef537e",
         .A = "9025e6183706105e948b1b0edf922f9011b9e11887d70adb00b26f272b9e76a38f3099084d9cccf12d04b1a99c0f654f8b9ed90c6dff9478c60bf05d58d734ab60eaefa14a22230ec60c90dc1f0704b61eef0bef345785ae0e6a9af7db069cf6bd2b4e0fe58a0ade83c7e46a04b9fe1d24cb9b65c6f80de713e61d70eae5b286",
         .E = "d7e6df5d755284929b986cd9b61c9c2c8843f24c711fbdbae1a468edcae159400943725570726cdc92b3ea94f9f206729516fdda83e31d815b0c7720e7598a91d992273e3bd8ac413b441d8f1dfe5aa7c3bf3ef573adc38292676217467731e6cf440a59611b8110af88d3e62f60209b513b01fbb69a097458ad02096b5e38f0",
         .M = "e4e784aa1fa88625a43ba0185a153a929663920be7fe674a4d33c943d3b898cff051482e7050a070cede53be5e89f31515772c7aea637576f99f82708f89d9e244f6ad3a24a02cbe5c0ff7bcf2dad5491f53db7c3f2698a7c41b44f086652f17bb05fe4c5c0a92433c34086b49d7e1825b28bab6c5a9bd0bc95b53d659afa0d7"
      },
      // See https://github.com/openssl/openssl/commit/e9e726506cd2a3fd9c0f12daf8cc1fe934c7dddb OpenSSL's test vectors do not include the expected value, so ModExp was computed with Python 3
      {
         .ModExp = "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",
         .A = "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",
         .E = "f95dc0f980fbd22e90caa5a387cc4a369f3f830d50dd321c40db8c09a7e1a241a536e096622d3280c0c1ba849c1f4a79bf490f60006d081e8cf69960189f0d312cd9e17073a3fba7881b21474a13b334116cb2f5dbf3189a6de3515d0840f053c776d3982d391b6d04d642dda5cc6d1640174c09875addb70595658f89efb439dc6fbd55f903aadd307982d3f659207f265e1ec6271b274521b7a5e28e8fd7a55df089292820477802a43cf5b6b94e999e8c9944ddebb0d0e95a60f88cb7e813ba110d20e1024774107dd02949031864923b3cb8c3f7250d6d1287b0a40db6a47bd5a469518eb65aa207ddc47d8c6e5fc8e0c105be8fc1d4b57b2e27540471d5",
         .M = "fef15d5ce4625f1bccfbba49fc8439c72bf8202af039a2259678941b60bb4a8f2987e965d58fd8cf86a856674d519763d0e1211cc9f8596971050d56d9b35db3785866cfbca17cfdbed6060be3629d894f924a89fdc1efc624f80d41a22f19009503fcc3824ef62ccb9208430c26f2d8ceb2c63488ec4c07437aa4c96c43dd8b9289ed00a712ff66ee195dc71f5e4ead02172b63c543d69baf495f5fd63ba7bcc633bd309c016e37736da92129d0b053d4ab28d21ad7d8b6fab2a8bbdc8ee647d2fbcf2cf426cf892e6f5639e0252993965dfb73ccd277407014ea784aaa280cb7b03972bc8b0baa72360bdb44b82415b86b2f260f877791cd33ba8f2d65229b"
      },
      // The following inputs trigger an edge case between Montgomery reduction and the "almost" reduction variant from https://eprint.iacr.org/2011/239
      {
         .ModExp = "00",
         .A = "19c7bc9b97c6083cd7b8d1cd001452c9b67983247169c6532047eb7fc8933014dbf69fee7a358769f1429802c8ea89d4f9ca6ba6f368fbdb1fa5717b4a00",
         .E = "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",
         .M = "519b6e57781d40d897ec0c1b648d195526726b295438c9a70928ac25979563d72db91c8c42298a33b572edecdf40904c68a23337aa5341b56e92b0da5041"
      },
      // To fully exercise BN_mod_exp_mont_consttime codepaths, we generate inputs at different bitwidths. rsaz-avx2.pl only runs at 1024-bit moduli, and
      // x86_64-mont5.pl unrolls 8 64-bit words at a time, so we want to capture both multiples of 512- and non-multiples. Also include moduli that are not quite a full word.
      // 512-bit
      {
         .ModExp = "00",
         .A = "8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e",
         .E = "ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
         .M = "8f42c9e9e351ba9b32ab0cf69da43f4acf7028d19cff6e5059ea0e3fcc97c97f36a31470044737d4c0c933ac441ecb29e32c81401523afdac7de9c3fd8493c97"
      },
      // 1024-bit
      {
         .ModExp = "00",
         .A = "800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000002f",
         .E = "ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
         .M = "9da8dc26fdf4d2e49833b240ee552beb7a6e251caa91bfb5d6cafaf8ed9461877fda8f6ac299036d35806bc1ae7872e54eaac1ec6bee6d02c6621a9cf8883b3abc33c49b3e601203e0e86ef8f0562412cc689ee2670704583909ca6d7774c9f9f9f4d77d37fedef9cb51d207cb629ec02fa03b526fd6594bfa8f2da71238a0b7"
      },
      // 1025-bit
      {
         .ModExp = "00",
         .A = "010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000011",
         .E = "ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
         .M = "010223abfdda02e84e11cec8ee7fc784fa135733935f7b9054bb70f1f06d234d76dcf3beed55c7f39e955dc1fef2b65009240fd02f7a1b27a78fc2867144bf666efb929856db9f671c356c4c67a068a70fe83c52eebda03668872fd270d0794f0771d217fb6b93b12529a944f7f0496a9158757c55b8ee14f803f1d2d887e2f561"
      },
      // 1088-bit
      {
         .ModExp = "00",
         .A = "8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003d",
         .E = "ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
         .M = "e91f6d748773cb212a23aa348125615123b1800c9ea222c9374c757702ae4140fa333790ed8f6bf60a1d7dda65c2767cc5f33e32e333d19fbfb5a2b85795757c9ca070268763a618e9d33873d28a89bf88acd209efbb15b80cd33b92a6b3a682e1c91782fc24fb86ddff4f809219c977b54b99359094bbcc51dfe17b992ab24b74a17950ad754281"
      },
      // 1472-bit
      {
         .ModExp = "00",
         .A = "8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001d",
         .E = "ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
         .M = "a8770362f4bfe4fc1ab0e52705c11a9b6ba235d5a5f22197c2d68e27ed18426ede3316af706aa79bcf943dbd51459eb15ae1f9386216b3f3a847f94440a65b97659bc5ba2adb67173714ecaa886c0b926d7a64ea45576f9d2171784ce7e801724d5b0abfd93357d538ea7ad3ad89a74f4660bdb66dfb5f684dcf00402e3cdf0ab58afd867c943c8f47b80268a789456aa7c50a619dd2f9f5e3f74b5d810f0f8dadbf4ad5b917cdcb156c4c132611c8b3b035118a9e03551f"
      },
      // 1536-bit
      {
         .ModExp = "00",
         .A = "800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000002",
         .E = "ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
         .M = "878cd000778f927b2f1a4b8bac86efd282079a7ac0d25e09ffd2f72fbc282e65e233929d2457c7b1d63c56fb706cdfa04fb87e654c578c98d7cf59c2293dc5641086b68db4867105981daaf147a0ee91f6932ef064deae4142c19e58d50c0686f0eaf778be72450f89a98b4680bbc5ffab942195e44dd20616150fd1deca058068ca31ab2f861e99082588f17a2025bf5e536150142fca3187a259c791fc721430f24d7e338f8dc02e693a7e694d42775e80f7f7c03600b6ae86b4aba2b0e991"
      },
      // 2048-bit
      {
         .ModExp = "00",
         .A = "8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000f",
         .E = "ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
         .M = "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"
      },
      // 3072-bit
      {
         .ModExp = "00",
         .A = "80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001d",
         .E = "ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
         .M = "c23dfd244a58a668d514498a705c8f8f548311b24f0f98b023d2d33632534c2ae948d6641d41fd7a29fbbd594bfc7fdd6e8162cbb3056af3075347b6fc8876458d33a9d0ffdbcdf482de0c73d1310fd8fa8f9f92dd0dbb0e2034e98a30f6c11b482f7476c5b593f673a322b1130daa4314e9074270dce1076436f0d56cf196afcbb235a9a7b3ac85b9062e85fc0e63a12c468c787019f6805f9faab64fc6a0babc80785d88740243f11366bffb40ccbe8b2bb7a99a2c8238a6f656bb0117d7b2602aa400f4d77de5f93c673f13264ca70de949454e3e3f261993c1aa427e8ef4f507af744f71f3b4aaf3c981d44cc1bfb1eb1151168762b242b740573df698e500d99612e17dc760f7b3bf7c235e39e81ad7edbe6c07dbb8b139745bb394d61cb799bcafec5de074932b0b2d74797e779ac8d81f63a2b2e9baa229dfaa7f90f34ffade1d2ad022a3407d35eb2d7477c6ae8ad100f6e95c05b4f947c1fabfb11a17add384e6b4cd3a02fd9b43f46805c6c74e366b74aa3b766be7a5fbbd67fa81"
      },
      // 4096-bit
      {
         .ModExp = "00",
         .A = "8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001",
         .E = "ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
         .M = "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"
      },
      // These are regression tests for code which historically reached the RSAZ-512 code. That has since been removed, but the test vectors remain.
      // Note that the lengths of the inputs, especially the *bit* length of |M|, matter a lot.
      // Control: No relationship between A and M except that A < M and they're the same number of limbs.
      {
         .ModExp = "7f34c1cd63377bc3abf2bb5b2d1bf5f06454e1e8040fe19a72245ce9731cbee1bf9e84532300776c8021ed4f3a8de508d85b4cf320bd82065a013754857b50c4",
         .A = "8e4e67da6ff890643d0599387955996ef6f0c2045eb9944576ddb965ca64cdb6247727ce128ef178d4a84e5a56d2e67eb0fe389ecbf691f9244ae80f4c11b364",
         .E =  "0be99d8f0650e540b9b191e9cf96f74881b902e32ed169ffd8a1776c3f3e80f0ac765aa14615713e1549f250a20fe4ee48c4e0c6176162fc7842a0dd64d640d1",
         .M = "f12f2c19ee1ecf2c999b87bdafde60eace3790faad8f9adec13b14c6dfb69f8795a1d0fe65494250b59534014b918453042012952ae6f5786342999600725491"
      },
      // A == M - 1 == -1 (mod M) and the exponent is odd so A ^ E (mod M) == A.
      {
         .ModExp = "f12f2c19ee1ecf2c999b87bdafde60eace3790faad8f9adec13b14c6dfb69f8795a1d0fe65494250b59534014b918453042012952ae6f5786342999600725490",
         .A = "f12f2c19ee1ecf2c999b87bdafde60eace3790faad8f9adec13b14c6dfb69f8795a1d0fe65494250b59534014b918453042012952ae6f5786342999600725490",
         .E =  "0be99d8f0650e540b9b191e9cf96f74881b902e32ed169ffd8a1776c3f3e80f0ac765aa14615713e1549f250a20fe4ee48c4e0c6176162fc7842a0dd64d640d1",
         .M = "f12f2c19ee1ecf2c999b87bdafde60eace3790faad8f9adec13b14c6dfb69f8795a1d0fe65494250b59534014b918453042012952ae6f5786342999600725491"
      },
      // A == M, so A == 0 (mod M) so A ^ E (mod M) == 0. Note that A mod M with a "correct top" isn't the right length for RSAZ.
      {
         .ModExp = "00",
         .A = "f12f2c19ee1ecf2c999b87bdafde60eace3790faad8f9adec13b14c6dfb69f8795a1d0fe65494250b59534014b918453042012952ae6f5786342999600725491",
         .E =  "0be99d8f0650e540b9b191e9cf96f74881b902e32ed169ffd8a1776c3f3e80f0ac765aa14615713e1549f250a20fe4ee48c4e0c6176162fc7842a0dd64d640d1",
         .M = "f12f2c19ee1ecf2c999b87bdafde60eace3790faad8f9adec13b14c6dfb69f8795a1d0fe65494250b59534014b918453042012952ae6f5786342999600725491"
      },
      //RSAZ 1024-bit.
      // Note that the lengths of the inputs, especially the *bit* length of |M|, matter a lot.
      // Control: No relationship between A and M except that A < M and they're the same number of limbs.
      {
         .ModExp = "8984f8c16044f9c0ad7bd72347af90f58e6e003acda92b76e3c7c4a56ea8e918409d8e9b34884d4c89d0b17cb40fe898f2627c084a0f1698e46beccbf6f48eecc281e11ea9e5135adba460ddae157f2c655b5f589ce29b254d43a960a71cede8a08dbb86be4dac22458da232fb1ec2470856827302ed772c9ddafa408c931aa7",
         .A = "21158da5fe20356825e72b3f5384ec57720d22f727b27ce2f945c8ee311db781add73bf8fae96b775c909bd22fca75c44c2b0584284a5bb1c07f8eefcd6b0a44047a02b185df34f897f11d4fb9a86c9eb841b4cb8d0383441fdc5af3ef385b5e8380f605d73ed41bb42eb2c2a5704d6034b3ad058dafffce83dbbfb6295daaf8",
         .E = "ecdebd112b3b5788669449dcddbd479a203ee9ab72a9bb9c406b97623513bf0ab9a22f1f23634d269e16bfd6d3b64202b71fc355057411967b6ac70f8d9cef0a4e06819a9a18cc06bbe438243fa9759303d98be8a65dc1cb13595ee9b99f138554425d50f6fbc025d8ffa3eaea828d6f3b82a3584146bafde34da257995f0575",
         .M = "ff3a3e023db3bba929ca4ededbace13d0d1264387b5ef62734e177eaf47a78af56b58aacc8ac5d46f5b066bafb95d93d4442bb948653613eec76837b4ffb7991cb080b6c8b403fb09bc817d026e283ee47ab2fc9af274b12f626eda2fe02004a8e27b9ed7d3b614e8955c7e7c2c0700edd079455237c4475fbd41857e206e4b7"
      },
      // A == M - 1 == -1 (mod M) and the exponent is odd so A ^ E (mod M) == A.
      {
         .ModExp = "b5d257b2c50b050d42f0852eff5cfa2571157c500cd0bd9aa0b2ccdd89c531c9609d520eb81d928fb52b06da25dc713561aa0bd365ee56db9e62ac6787a85936990f44438363560f7af9e0c16f378e5b83f658252390d849401817624da97ec613a1b855fd901847352f434a777e4e32af0cb4033c7547fb6437d067fcd3d964",
         .A =  "b5d257b2c50b050d42f0852eff5cfa2571157c500cd0bd9aa0b2ccdd89c531c9609d520eb81d928fb52b06da25dc713561aa0bd365ee56db9e62ac6787a85936990f44438363560f7af9e0c16f378e5b83f658252390d849401817624da97ec613a1b855fd901847352f434a777e4e32af0cb4033c7547fb6437d067fcd3d964",
         .E = "61803d4973ae68cfb2ba6770dbed70d36760fa42c01a16d1482eacf0d01adf7a917bc86ece58a73b920295c1291b90f49167ef856ecad149330e1fd49ec71392fb62d47270b53e6d4f3c8f044b80a5736753364896932abc6d872c4c5e135d1edb200597a93ceb262ff6c99079177cd10808b9ed20c8cd7352d80ac7f6963103",
         .M =  "b5d257b2c50b050d42f0852eff5cfa2571157c500cd0bd9aa0b2ccdd89c531c9609d520eb81d928fb52b06da25dc713561aa0bd365ee56db9e62ac6787a85936990f44438363560f7af9e0c16f378e5b83f658252390d849401817624da97ec613a1b855fd901847352f434a777e4e32af0cb4033c7547fb6437d067fcd3d965"
      },
      // # A == M, so A == 0 (mod M) so A ^ E (mod M) == 0. Note that A mod M with a "correct top" isn't the right length for RSAZ.
      {
         .ModExp = "00",
         .A =  "b5d257b2c50b050d42f0852eff5cfa2571157c500cd0bd9aa0b2ccdd89c531c9609d520eb81d928fb52b06da25dc713561aa0bd365ee56db9e62ac6787a85936990f44438363560f7af9e0c16f378e5b83f658252390d849401817624da97ec613a1b855fd901847352f434a777e4e32af0cb4033c7547fb6437d067fcd3d965",
         .E = "61803d4973ae68cfb2ba6770dbed70d36760fa42c01a16d1482eacf0d01adf7a917bc86ece58a73b920295c1291b90f49167ef856ecad149330e1fd49ec71392fb62d47270b53e6d4f3c8f044b80a5736753364896932abc6d872c4c5e135d1edb200597a93ceb262ff6c99079177cd10808b9ed20c8cd7352d80ac7f6963103",
         .M =  "b5d257b2c50b050d42f0852eff5cfa2571157c500cd0bd9aa0b2ccdd89c531c9609d520eb81d928fb52b06da25dc713561aa0bd365ee56db9e62ac6787a85936990f44438363560f7af9e0c16f378e5b83f658252390d849401817624da97ec613a1b855fd901847352f434a777e4e32af0cb4033c7547fb6437d067fcd3d965"
      },
      // Regression test for CVE-2017-3738.
      {
         .ModExp = "d360792bd8210786607817c3dda64cc38c8d0f25569597cb1f363c7919a0c3587baff01a2283edaeb04fc288ac0ab3f279b2a89ffcb452d8bdf72422a9f9780f4aa702dc964cf033149d3a339883062cab8564aebdbfac0bf68985e522c6fe545b346044690c525ca85d3f4eb3e3c25cdf541545afc84a309e9b1d7807003461",
         .A = "ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff2020202020df",
         .E = "2020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020FF2020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020202020",
         .M = "ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff2020202020ff"
      },
      // Test vectors for CVE-2019-1551. (We do not carry the assembly file with the bug, but we use the test vectors anyway.)
      // Original test vectors by OSS-Fuzz.
      {
         .ModExp = "9d675d188a07e9bd1b32638cc8cfd5002ef89bd1a9648f806567b87939140a67977dc8da17323b8e4c6bc53875cda8b656df8f54cc32e44fd9c21d122ea3c0d6",
         .A = "dea9b3e0b44ae67b2ac9b7c2b18eeb4dab206b014981a46ac409f195eeb6896f132cf8497c87d1188008ee511054ebb426203355b7d515dce9501cb759ac1373",
         .E = "0b01ae745b101e9e45ec05dcff72e7f8fc04c79ffe324301fda0b4f7be81d85c4e875c73fc6c5cb40000000000000000000000000000000000",
         .M = "ffffffff01ffffffffffffffffffffffffffe2000000000000000000000000000010fab8d960706cd4c21818115650cad61d4f10da325dffffffff00ffff00ff"
      },
      {
         .ModExp = "651f811b62ee8770e3598c340864dd6b0be9bb6376b6f933ab216fd55538e6ad1000cb2b3c64f54d554e004b6eec8138e6ecff00452d443a42041b72e6cd9ead",
         .A = "3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e",
         .E = "3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e3e09003e3e3e3e3e3e3e3e3e3e3e3e3e3e010900230a01230a2100ffffff0000adf300a58700000000ffffff00",
         .M = "ffffff0b00000000000000000000000000ffffffff0000ffffffff00000a0000000a00000000000000000000ffffffff000000000000ffffffffffff000000ff"
      },
      // Test vectors for rsaz_512_sqr bug, with rcx/rbx=1
      // between first and second iteration
      {
         .ModExp = "01",
         .A = "624e6a171024e6a171024e6a171024e6a171024e6a171024e6a171024e6a171024e6a171024e6a171024e6a171024e6a14ce297f2873536f959d8c3390d973b6",
         .E = "8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006e",
         .M = "8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006f"
      },
      //between second and third iteration
      {
         .ModExp = "01",
         .A = "11024e6a171024e6a171024e6a171024e6a171024e6a171024e6a171024e6a171024e6a171024e6a14ce297f2873536f959d8c3390d97360800000000000000f",
         .E = "8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006e",
         .M = "8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006f"
      },
      // between third and fourth iteration
      {
         .ModExp = "01",
         .A = "4171024e6a171024e6a171024e6a171024e6a171024e6a171024e6a171024e6a14ce297f2873536f959d8c3390d9736080000000000000000000000000000039",
         .E = "8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006e",
         .M = "8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006f"
      },
      // between fourth and fifth iteration
      {
         .ModExp = "01",
         .A = "06a171024e6a171024e6a171024e6a171024e6a171024e6a14ce297f2873536f959d8c3390d97360800000000000000000000000000000000000000000000006",
         .E = "8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006e",
         .M = "8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006f"
      },
      // between fifth and sixth iteration
      {
         .ModExp = "01",
         .A = "44e6a171024e6a171024e6a171024e6a14ce297f2873536f959d8c3390d97360800000000000000000000000000000000000000000000000000000000000003c",
         .E = "8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006e",
         .M = "8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006f"
      },
      // between sixth and seventh iteration
      {
         .ModExp = "01",
         .A = "1024e6a171024e6a14ce297f2873536f959d8c3390d973608000000000000000000000000000000000000000000000000000000000000000000000000000000e",
         .E = "8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006e",
         .M = "8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006f"
      },
      // between seventh and eighth iteration
      {
         .ModExp = "01",
         .A = "626eee5e3c8653be47ed15e84b97cc7f800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000187",
         .E = "c00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000002f8",
         .M = "c00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000002f9"
      },
      // Test vectors for rsaz_512_srq bug, with rcx/rbx=2
      // between first and second iteration
      {
         .ModExp = "01",
         .A = "3c40939a85c40939a85c40939a85c40939a85c40939a85c40939a85c40939a85c40939a85c40939a85c40939a85c4093995e8efdb195e8efd8caf477ed8caf7c",
         .E = "8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006e",
         .M = "8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006f"
      },
      // between second and third iteration
      {
         .ModExp = "01",
         .A = "485c40939a85c40939a85c40939a85c40939a85c40939a85c40939a85c40939a85c40939a85c4093995e8efdb195e8efd8caf477ed8caf47800000000000003f",
         .E = "8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006e",
         .M = "8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006f"
      },
      // between third and forth iteration
      {
         .ModExp = "01",
         .A = "59a85c40939a85c40939a85c40939a85c40939a85c40939a85c40939a85c4093995e8efdb195e8efd8caf477ed8caf478000000000000000000000000000004e",
         .E = "8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006e",
         .M = "8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006f"
      },
      // between forth and fifth iteration
      {
         .ModExp = "01",
         .A = "2939a85c40939a85c40939a85c40939a85c40939a85c4093995e8efdb195e8efd8caf477ed8caf47800000000000000000000000000000000000000000000024",
         .E = "8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006e",
         .M = "8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006f"
      },
      // between fifth and sixth iteration
      {
         .ModExp = "01",
         .A = "640939a85c40939a85c40939a85c4093995e8efdb195e8efd8caf477ed8caf478000000000000000000000000000000000000000000000000000000000000057",
         .E = "8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006e",
         .M = "8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006f"
      },
      // between sixth and seventh iteration
      {
         .ModExp = "01",
         .A = "25c40939a85c4093995e8efdb195e8efd8caf477ed8caf4780000000000000000000000000000000000000000000000000000000000000000000000000000021",
         .E = "8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006e",
         .M = "8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006f"
      },
      // between seventh and eighth iteration
      {
         .ModExp = "01",
         .A = "7b4919849931b28a14fcace213f2b3884fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff84b6e67b66ce4d9c",
         .E = "ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff000000000000004c",
         .M = "ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff000000000000004d"
      }
   };

   for(const modexp_test_params& test : tests) {
      const bytes base = to_bytes(test.A);
      const bytes exponent = to_bytes(test.E);
      const bytes modulus = to_bytes(test.M);

      bytes expected_result = to_bytes(test.ModExp);
      //the host function's result is always length of modulus; pad expected result with enough 0x00s to match up
      expected_result.insert(expected_result.begin(), modulus.size() - expected_result.size(), 0x00);

      BOOST_CHECK_EQUAL(std::get<bytes>(fc::modexp(base, exponent, modulus)), expected_result);
   }

} FC_LOG_AND_RETHROW();

BOOST_AUTO_TEST_CASE(modexp_benchmarking) try {

    std::mt19937 r(0x11223344);

    auto generate_random_bytes = [](std::mt19937& rand_eng, unsigned int num_bytes) {
        std::vector<char> result(num_bytes);

        uint_fast32_t v = 0;
        for(int byte_pos = 0, end = result.size(); byte_pos < end; ++byte_pos) {
            if ((byte_pos & 0x03) == 0) { // if divisible by 4
                v = rand_eng();
            }
            result[byte_pos] = v & 0xFF;
            v >>= 8;
        }

        return result;
    };

    static constexpr unsigned int num_trials = 10; // 10000

    static_assert(num_trials > 0);

    static constexpr unsigned int bit_calc_limit = 101; // 120

    static constexpr unsigned int start_num_bytes = 1;
    static constexpr unsigned int end_num_bytes   = 1 << ((bit_calc_limit + 7)/8);

    static_assert(start_num_bytes <= end_num_bytes);

    struct statistics {
        unsigned int modulus_bit_size;  // bit size of modulus and base
        unsigned int exponent_bit_size; // bit size of exponent
        int64_t      min_time_ns;
        int64_t      max_time_ns;
        int64_t      avg_time_ns;
    }; 

    std::vector<statistics> stats;

    auto ceil_log2 = [](uint32_t n) -> uint32_t {
        if (n <= 1) {
            return 0;
        }
        return 32 - __builtin_clz(n - 1);
    };

    BOOST_CHECK(ceil_log2(0) == 0);
    BOOST_CHECK(ceil_log2(1) == 0);
    BOOST_CHECK(ceil_log2(2) == 1);
    BOOST_CHECK(ceil_log2(3) == 2);
    BOOST_CHECK(ceil_log2(4) == 2);
    BOOST_CHECK(ceil_log2(5) == 3);
    BOOST_CHECK(ceil_log2(15) == 4);
    BOOST_CHECK(ceil_log2(16) == 4);
    BOOST_CHECK(ceil_log2(17) == 5);

    for (unsigned int n = start_num_bytes; n <= end_num_bytes; n *= 2) {
        unsigned int bit_calc = 8 * ceil_log2(n);
        for (unsigned int exponent_num_bytes = 1; 
             exponent_num_bytes <= 2*n && bit_calc <= bit_calc_limit; 
             exponent_num_bytes *= 2, bit_calc += 5) 
        {
            int64_t min_duration_ns = std::numeric_limits<int64_t>::max();
            int64_t max_duration_ns = 0;
            int64_t total_duration_ns = 0;

            for (unsigned int trial = 0; trial < num_trials; ++trial) {
                auto base     = generate_random_bytes(r, n);
                auto exponent = generate_random_bytes(r, exponent_num_bytes);
                auto modulus  = generate_random_bytes(r, n);

                auto start_time = std::chrono::steady_clock::now();

                auto res = fc::modexp(base, exponent, modulus);

                auto end_time = std::chrono::steady_clock::now();

                int64_t duration_ns = std::chrono::duration_cast<std::chrono::nanoseconds>(end_time - start_time).count();

                //ilog("(${base})^(${exp}) % ${mod} = ${result} [took ${duration} ns]", 
                //     ("base", base)("exp", exponent)("mod", modulus)("result", std::get<bytes>(res))("duration", duration_ns)
                //    );

                min_duration_ns = std::min(min_duration_ns, duration_ns);
                max_duration_ns = std::max(max_duration_ns, duration_ns);
                total_duration_ns += duration_ns;
            }

            stats.push_back(statistics{
                .modulus_bit_size  = n * 8,
                .exponent_bit_size = exponent_num_bytes * 8, 
                .min_time_ns       = min_duration_ns,
                .max_time_ns       = max_duration_ns,
                .avg_time_ns       = (total_duration_ns / num_trials),
            });

            const auto& stat = stats.back();

            ilog("Completed random runs of mod_exp with ${bit_width}-bit width base and modulus values and "
                 "${exp_bit_width}-bit width exponent values. "
                 "Min time: ${min} ns; Average time: ${avg} ns; Max time: ${max} ns.",
                ("bit_width", stat.modulus_bit_size)("exp_bit_width", stat.exponent_bit_size)
                ("min", stat.min_time_ns)("avg", stat.avg_time_ns)("max", stat.max_time_ns)
                );

        }
    }

    std::string stats_output = "Table (in csv format) summarizing statistics from runs:\n";
    stats_output += "Modulus/Base Bit Size,Exponent Bit Size,Average Time (ns)\n";
    for (const auto& stat : stats) {
        stats_output += std::to_string(stat.modulus_bit_size);
        stats_output += ',';
        stats_output += std::to_string(stat.exponent_bit_size);
        stats_output += ',';
        stats_output += std::to_string(stat.avg_time_ns);
        stats_output += '\n';
    }

    ilog(stats_output);

    // Running the above benchmark (using commented values for num_trials and bit_calc_limit) with a release build on 
    // an AMD 3.4 GHz CPU provides average durations for executing mod_exp for varying bit sizes for the values 
    // (but with base and modulus bit sizes kept equal to one another).

    // Holding the base/modulus bit size constant and increasing the exponent bit size shows a linear relationship with increasing bit
    // size on the average time to execute the modular exponentiation. The slope of the best fit line to the empirical data appears
    // to scale super-linearly with base/modulus size. A quadratic (degree 2) fit works okay, but it appears that a better fit is to
    // model the slope of the linear relationship between average time and exponent bit size as a the base/modulus bit size taken to
    // the 1.6 power and then scaled by some constant.

    // Holding the exponent bit size constant and increasing the base/modulus bit size shows a super-linear relationship with
    // increasing bit size on the average time to execute the modular exponentiation. A quadratic relationship works pretty well
    // but perhaps a fractional exponent between 1 and 2 (e.g. 1.6) would work well as well.
    
    // What is particularly revealing is plotting the average time with respect to some combination of the bit sizes of base/modulus and
    // exponent. If the independent variable is the product of the exponent bit size and the base/modulus bit size, the correlation is
    // not great. Even if the independent variable is the product of the exponent bit size and the base/modulus bit size taken to some power,
    // the correlation is still not great.
    // It seems that trying to capture all the data using a model like that breaks down when the exponent bit size is greater than the
    // base/modulus bit size.
    // If we filter out all the data points where the exponent bit size is greater than the base/modulus bit size, and then choose as
    // then independent variable the product of the exponent bit size and the base/modulus bit size taken to some power, then we get
    // a pretty good linear correlation when a power of 1.6 is chosen.

    // TODO: See if theoretical analysis of the modular exponentiation algorithm also justifies these scaling properties.

    // Example results for average time:
    // | Modulus/Base Bit Size | Exponent Bit Size | Average Time (ns) |
    // | --------------------- | ----------------- | ----------------- |
    // | 2048                  | 32                |             33826 |
    // | 2048                  | 256               |            250067 |
    // | 2048                  | 2048              |           1891095 |
    // | 4096                  | 32                |            129181 |
    // | 4096                  | 256               |            954024 |
    // | 4096                  | 2048              |           7205115 |
    // | 8192                  | 32                |            347938 |
    // | 8192                  | 256               |           2503652 |
    // | 8192                  | 2048              |          19199775 |

    // The empirical results show that the average time stays well below 5 ms if the exponent bit size does not exceed the
    // modulus/base bit size and the product of the exponent bit size and the 
    // (modulus/base bit size)^1.6 does not exceed 550,000,000.
    // Another way of satisfying that constraint is to require that the 5*ceil(log2(exponent bit size)) + 8*ceil(log2(modulus bit size)) 
    // be less than or equal to 5*floor(log2(500000000)) = 145.
    // Or equivalently, assuming the bit sizes are multiples of 8:
    // 5*ceil(log2(exponent bit size/8)) + 8*ceil(log2(modulus bit size/8)) <= 106.

    // Take, as an example, a 8192-bit modulus/base and a 128-bit exponent (which on average took 1.29 ms).
    // 5*ceil(log2(128)) + 8*ceil(log2(8192)) = 5*7 + 8*13 = 139 which is less than the limit of 145.
    // 
    // Or, as an other example, a 2048-bit modulus/base and a 2048-bit exponent (which on average took 1.89 ms).
    // 5*ceil(log2(2048)) + 8*ceil(log2(2048)) = 5*11 + 8*11 = 143 which is less than the limit of 145.
    //
    // On the other hand, consider a 4096-bit modulus/base and a 1024-bit exponent (which on average took 3.69 ms).
    // 5*ceil(log2(1024)) + 8*ceil(log2(4096)) = 5*10 + 8*12 = 146 which is greater than the limit of 145.

} FC_LOG_AND_RETHROW();

BOOST_AUTO_TEST_SUITE_END()